Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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# Variance

```back to [[Statistical Dispersion]]

The '''variance'''  of a set of data is the mean of the sum of squared deviations from the [[Arithmetic Mean]] of the same set of data. Because this calculation sums the squared deviations, the unit of variance is the square of the unit of observation. Thus, the variance of a set of heights measured in inches will be given in square inches. This fact is inconvenient and has motivated statisticians to call the square root of the variance, the [[Standard Deviation]] and to quote this value as a summary of dispersion.

When the set of data is a [[Population]], we call this the ''population variance''. If the set is a [[Sample]], we call it the ''sample variance''.

The method of calculation is easily understood from the table below where the mean is 8.

i   x[i]   x[i]-mean   (x[i]-mean)^2
1     5        -3            9
2     7        -1            1
3     8         0            0
4    10         2            4
5    10         2            4
---  ----       ---          ---
n=5  sum=40      0           18

mean = 40/5 = 8
variance = 18/5 = 3.6
standard deviation = 1.897366596101

Note that the column of deviations sums to zero. This is always the case.
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[[Dick Beldin]]
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